Concept explainers
True or False? Justify your answer with a proof or a counterexample.
310. A function is always one-to-one.
To calculate: Justify the statement with a proof or a counterexample
“A function is always one-to-one.”
Answer to Problem 310RE
The statement “A function is always one-to-one” is false.
Explanation of Solution
Given information: Given statement is “A function is always one-to-one.”
Formula used: A function is said to be one-to-one, if every element of the range of the function corresponds to exactly one element of the domain.
For a function to be one-to one
If
Then
Calculation:
Let us consider an example.
Let
This implies that
Thus, for element in range, there exists two elements in domain.
Hence, the function is not always one-to-one.
Conclusion:
Hence, the statement “A function is always one-to-one” is false.
Want to see more full solutions like this?
Chapter 1 Solutions
Calculus Volume 1
Additional Math Textbook Solutions
Introductory Statistics
Using & Understanding Mathematics: A Quantitative Reasoning Approach (7th Edition)
Probability and Statistics for Engineers and Scientists
Using and Understanding Mathematics: A Quantitative Reasoning Approach (6th Edition)
Thinking Mathematically (7th Edition)
Mathematics All Around (6th Edition)
- Describe why the horizontal line test is an effective way to determine whether a function is one-to-one?arrow_forwardUse your schools library, the Internet, or some other reference source to find real-life applications of approximations of functions.arrow_forwardWhen examining the formula of a function that is the result of multiple transformations, how can you tell a horizontal stretch from a vertical stretch?arrow_forward
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillElementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCollege Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage LearningCollege AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning